Which is greater, the total volume of three spheres, each of which has a diameter 5 in., the volume of one sphere that has a diameter 8 in., or the volume of a hemisphere with a diameter of 10 in.?

a) The volume of three spheres, each with a diameter of 5 inches, is greater.
b) The volume of one sphere with a diameter of 8 inches is greater.
c) The volume of the hemisphere with a diameter of 10 in. is greater.
d) The three volumes are the same.

Answer:

Here is my answers for the practice that I have come across. It may be the new one. I also shortened it.
1. find the SA of a grape fruit with a c of 14cm.
62 cm^2
2. a sphere has a volume of 900 ci. find SA
451
3. a solid metal cube with an edge length of 9 in is melted and reshaped into a sphere. which is SA of sphere
391.7
4. the sphere below fits snugly inside a cube with 6 in edges what is the v of the space between the sphere and the cube
102.9
5. find the v in terms of pi of a sphere with a SA of 9 pi square feet
9/2 pi ft^3
6. which of the following is the greatest the total v of 3 sphere each of which a diameter of 5 in the v of one sphere that has a diameter 8 in or the v of a hemisphere with a diameter of 10 in
the v of 1 sphere with a diameter of 8 in is greatest
7. a sphere has center 0 0 0 and a radius of 5
0 -3 4
8. find v of figure the diameter of the base is 4 cm
46/3 pi cm^3
9. a sphere with a radius of 5 cm fits inside a box every face is tangent to the sphere
6 pi
10. tennis balls are sold in packs of 3 and come packaged in a plastic cylindrical container there is no space between
69 square inches
Step-by-step explanation:

3 small ones of 5 in diameter

v = 3((4/3)π(2.5)^3) = 125π/2 = 62.5π = appr 196.35

one of diameter 8
v = (4/3)π(4^3) = 256π/3 = appr 268.08

hemisphere of radius 5
= (1/2)(4/3)π(5^3) = 250π/3 = appr 261.8

Oh cool he's right

well, just check. a sphere with diameter d has volume π/6 d^3

3*(π/6)(5^3) = 375π/6
(π/6)*8^3 = 512π/6
π/12 * 10^3 = 500π/6

Thank you, I had gotten it:)

Well, let's break it down, shall we? The volume of a sphere is given by the formula (4/3)πr^3, where r is the radius. So, for a sphere with a diameter of 5 inches, the radius is 2.5 inches.

The volume of one sphere with a diameter of 8 inches would have a radius of 4 inches.

And finally, the volume of a hemisphere - which is half of a sphere - with a diameter of 10 inches would have a radius of 5 inches.

So, if we calculate the volumes, we get:

Volume of three spheres: (4/3)π * 2.5^3 * 3 ≈ 65.4π cubic inches

Volume of one sphere: (4/3)π * 4^3 ≈ 268.1π cubic inches

Volume of hemisphere: (2/3)π * 5^3 ≈ 523.6π / 2 = 261.8π cubic inches

Now, to answer the question with a little clowny twist...

The volume of the three spheres is certainly not "small fry", but it's not quite as "spherically magnificent" as the single sphere with a diameter of 8 inches. And as for the hemisphere with a diameter of 10 inches? Well, it's halfway there, but it falls just short of being the "big cheese" in this scenario.

So, after all that mathematical hilarity, the correct answer is b) The volume of one sphere with a diameter of 8 inches is greater.

To compare the volumes of these shapes, we need to first calculate the volumes of each.

The volume of a sphere can be calculated using the formula V = (4/3)πr^3, where r is the radius of the sphere. The diameter of a sphere is twice the radius, so in this case, the radius of each of the three spheres with a diameter of 5 inches is 2.5 inches.

Let's calculate the volume of one of these spheres:
V1 = (4/3)π(2.5 in.)^3

Next, let's calculate the volume of a sphere with a diameter of 8 inches. Using the same formula, the radius of this sphere is 4 inches.
V2 = (4/3)π(4 in.)^3

Finally, let's calculate the volume of a hemisphere with a diameter of 10 inches. The radius of a hemisphere is half the diameter, so in this case, it's 5 inches.
V3 = (1/2)(4/3)π(5 in.)^3

Now, we can compare the volumes by comparing the values of V1, V2, and V3.

If V1 > V2 and V1 > V3, then the volume of three spheres with a diameter of 5 inches is greater.
If V2 > V1 and V2 > V3, then the volume of one sphere with a diameter of 8 inches is greater.
If V3 > V1 and V3 > V2, then the volume of the hemisphere with a diameter of 10 inches is greater.
If V1 = V2 = V3, then the volumes are the same.

Let's calculate the volumes and compare them.